equatorial coordinate system

Top

Home > Library > Miscellaneous > Columbia Encyclopedia

equatorial coordinate system, the most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere. The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox, the point at which the sun crosses the celestial equator in March.

To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle, analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0^h and declination 0°.

Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time. The angular distance from the sigma point to a star's hour circle is called its hour angle; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.

Equatorial coordinate system

Top

Home > Library > Miscellaneous > Wikipedia

The equatorial coordinate system is a widely-used method of specifying the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the center of the Earth, a fundamental plane consisting of the projection of the Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention.^[1]^[2]

The equatorial coordinate system in spherical coordinates. The fundamental plane is formed by projection of the Earth's equator onto the celestial sphere, forming the celestial equator (blue). The primary direction is established by projecting the Earth's orbit onto the celestial sphere, forming the ecliptic {red), and setting up the ascending node of the ecliptic on the celestial equator, the vernal equinox. Right ascensions are measured eastward along the celestial equator from the equinox, and declinations are measured positive northward from the celestial equator - two such coordinate pairs are shown here. Projections of the Earth's north and south geographic poles form the north and south celestial poles, respectively.

The origin at the center of the Earth means the coordinates are geocentric, that is, as seen from the center of the Earth as if it were transparent and nonrefracting.^[3] The fundamental plane and the primary direction mean that the coordinate system, while aligned with the Earth's equator and pole, does not rotate with the Earth, but remains relatively fixed against the background stars. A right-handed convention means that coordinates are positive toward the north and toward the east in the fundamental plane.

Contents

1 Primary direction
2 Spherical coordinates
3 Rectangular coordinates
- 3.1 Geocentric equatorial coordinates
- 3.2 Heliocentric equatorial coordinates
4 See also
5 External links
6 References

Primary direction

Spherical coordinates

Use in astronomy

A star's spherical coordinates are often expressed as a pair, right ascension and declination, without a distance coordinate. Because of the great distances to most celestial objects, astronomers often have little or no information on their exact distances, and hence use only the direction. The direction of sufficiently distant objects is the same for all observers, and it is convenient to specify this direction with the same coordinates for all. In contrast, in the horizontal coordinate system, a star's position differs from observer to observer based on their positions on the Earth's surface, and is continuously changing with the Earth's rotation.

Telescopes equipped with equatorial mounts and setting circles employ the equatorial coordinate system to find objects. Setting circles in conjunction with a star chart or ephemeris allow the telescope to be easily pointed at known objects on the celestial sphere.

As seen from above the Earth's north pole, a star's local hour angle (LHA) for an observer near New York (red). Also depicted are the star's right ascension and Greenwich hour angle (GHA), the local mean sidereal time (LMST) and Greenwich mean sidereal time (GMST). The symbol ʏ identifies the vernal equinox direction.

Declination

Main article: Declination

Declination (symbol $\delta$ , abbreviated dec) measures the angular distance of an object perpendicular to the celestial equator, positive to the north, negative to the south. For example, the north celestial pole has a declination of +90°. Declination is analogous to terrestrial latitude.^[6]^[7]^[8]

Right ascension

Main article: Right ascension

Right ascension (symbol $\alpha$ , abbreviated RA) measures the angular distance of an object eastward along the celestial equator from the vernal equinox to the hour circle passing through the object. The vernal equinox point is one of the two where the ecliptic intersects the celestial equator. Analogous to terrestrial longitude, right ascension is usually measured in sidereal hours, minutes and seconds instead of degrees, a result of the method of measuring right ascensions by timing the passage of objects across the meridian as the Earth rotates. There are (360° / 24^h) = 15° in one hour of right ascension, 24^h of right ascension around the entire celestial equator.^[6]^[9]^[10]

Hour angle

Main article: Hour angle

Alternatively to right ascension, hour angle (abbreviated HA or LHA, local hour angle), a left-handed system, measures the angular distance of an object westward along the celestial equator from the observer's meridian to the hour circle passing through the object. Unlike right ascension, hour angle is always increasing with the rotation of the Earth. Hour angle may be considered a means of measuring the time since an object crossed the meridian. A star on the observer's celestial meridian is said to have a zero hour angle. One sidereal hour later (approximately 0.9973 solar hours later), the Earth's rotation will carry the star to the west of the meridian, and its hour angle will be +1^h. When calculating topocentric phenomena, right ascension may be converted into hour angle as an intermediate step.^[11]^[12]^[13]

Rectangular coordinates

Geocentric equatorial coordinates

Geocentric equatorial coordinates. The origin is the center of the Earth. The fundamental plane is the plane of the Earth's equator. The primary direction (the x axis) is the vernal equinox. A right-handed convention specifies a y axis 90° to the east in the fundamental plane; the z axis is the north polar axis. The reference frame does not rotate with the Earth, rather, the Earth rotates around the z axis.

There are a number of rectangular variants of equatorial coordinates. All have:

The origin at the center of the Earth.
The fundamental plane in the plane of the Earth's equator.
The primary direction (the x axis) toward the vernal equinox, that is, the place where the Sun crosses the celestial equator in a northward direction in its annual apparent circuit around the ecliptic.
A right-handed convention, specifying a y axis 90° to the east in the fundamental plane and a z axis along the north polar axis.

The reference frames do not rotate with the Earth, remaining always directed toward the equinox, and drifting over time with the motions of precession and nutation.

In astronomy:^[14]
- The position of the Sun is often specified in the geocentric equatorial rectangular coordinates $X$ , $Y$ , $Z$ and a fourth distance coordinate, $R\ (= \sqrt{X^2 + Y^2 + Z^2})$ , in units of the astronomical unit.
- The positions of the planets and other Solar System bodies are often specified in the geocentric equatorial rectangular coordinates $\xi$ , $\eta$ , $\zeta$ and a fourth distance coordinate, $\mathit{\Delta}\ (= \sqrt{\xi^2 + \eta^2 + \zeta^2})$ , in units of the astronomical unit.

These rectangular coordinates are related to the corresponding spherical coordinates by

${X \over R}$ or ${\xi \over \mathit{\Delta}} = \cos \delta \cos \alpha$

${Y \over R}$ or ${\eta \over \mathit{\Delta}} = \cos \delta \sin \alpha$

${Z \over R}$ or ${\zeta \over \mathit{\Delta}} = \sin \delta$ .

In astrodynamics:^[15]
- The positions of artificial Earth satellites are specified in geocentric equatorial coordinates, also known as geocentric equatorial inertial (GEI), Earth-centered inertial (ECI), and conventional inertial system (CIS), all of which are equivalent in definition to the astronomical geocentric equatorial rectangular frames, above. In the geocentric equatorial frame, the x, y and z axes are often designated $I$ , $J$ and $K$ , respectively, or the frame's basis is specified by the unit vectors $\hat I$ , $\hat J$ and $\hat K$ .
- The Geocentric Celestial Reference Frame (GCRF) is the geocentric equivalent of the International Celestial Reference Frame (ICRF). Its primary direction is the equinox of J2000.0, and does not move with precession and nutation, but it is otherwise equivalent to the above systems.

**Summary of notation for astronomical equatorial coordinates**^[16]
	spherical			rectangular
	right ascension	declination	distance	general	special-purpose
geocentric	$\alpha$	$\delta$	$\mathit{\Delta}$	$\xi$ , $\eta$ , $\zeta$	$X$ , $Y$ , $Z$ (Sun)
heliocentric				$x$ , $y$ , $z$

Heliocentric equatorial coordinates

In astronomy, there is also a heliocentric rectangular variant of equatorial coordinates, designated $x$ , $y$ , $z$ , which has:

The origin at the center of the Sun.
The fundamental plane in the plane of the Earth's equator.
The primary direction (the $x$ axis) toward the vernal equinox.
A right-handed convention, specifying a $y$ axis 90° to the east in the fundamental plane and a $z$ axis along Earth's north polar axis.

This frame is in every way equivalent to the $\xi$ , $\eta$ , $\zeta$ frame, above, except that the origin is removed to the center of the Sun. It is commonly used in planetary orbit calculation. The three astronomical rectangular coordinate systems are related by

$\xi = x + X$

$\eta = y + Y$

$\zeta = z + Z$ .^[17]

External links

MEASURING THE SKY A Quick Guide to the Celestial Sphere James B. Kaler, University of Illinois
Celestial Equatorial Coordinate System University of Nebraska-Lincoln
Celestial Equatorial Coordinate Explorers University of Nebraska-Lincoln

References

^ Nautical Almanac Office, U.S. Naval Observatory; H.M. Nautical Almanac Office, Royal Greenwich Observatory (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. H.M. Stationery Office, London. pp. 24, 26.
^ Vallado, David A. (2001). Fundamentals of Astrodynamics and Applications. Microcosm Press, El Segundo, CA. p. 157. ISBN 1-881883-12-4.
^ U.S. Naval Observatory Nautical Almanac Office, Nautical Almanac Office; U.K. Hydrographic Office, H.M. Nautical Almanac Office (2008). The Astronomical Almanac for the Year 2010. U.S. Govt. Printing Office. p. M2, "apparent place". ISBN [[Special:BookSources/9700707740829|9700707740829]].
^ Explanatory Supplement (1961), pp. 20, 28
^ Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell, Inc., Richmond, VA. p. 137. ISBN 0-943396-35-2.
^ ^a ^b Peter Duffett-Smith. Practical Astronomy with Your Calculator, third edition. Cambridge University Press. pp. 28–29. ISBN 0-521-35699-7.
^ Meir H. Degani (1976). Astronomy Made Simple. Doubleday & Company, Inc. p. 216. ISBN 0-385-08854-X.
^ Astronomical Almanac 2010, p. M4
^ Moulton, Forest Ray (1918). "An Introduction to Astronomy". pp. 127. http://books.google.com/books?id=PJoUAQAAMAAJ&dq=astronomy+moulton&source=gbs_navlinks_s. , at Google books
^ Astronomical Almanac 2010, p. M14
^ Peter Duffett-Smith. Practical Astronomy with Your Calculator, third edition. Cambridge University Press. pp. 34–36. ISBN 0-521-35699-7.
^ Astronomical Almanac 2010, p. M8
^ Vallado (2001), p. 154
^ Explanatory Supplement (1961), pp. 24-26
^ Vallado (2001), pp. 157, 158
^ Explanatory Supplement (1961), sec. 1G
^ Explanatory Supplement (1961), pp. 20, 27

v t e Celestial coordinate systems

Horizontal coordinate system · Equatorial coordinate system · Ecliptic coordinate system · Galactic coordinate system · Supergalactic coordinate system

See also: Coordinate system · Converting coordinates

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Donate to Wikimedia

Help us answer these

Why cartesian coordinate system has a system?

The geocentric-equatorial coordinate system is used for interplanetary spacecraft?

What are coordinate systems?

Explain in detail about geocentric-equatorial coordinate system which is based on the earth's equatorial plane?

Post a question - any question - to the WikiAnswers community:

Copyrights:

Cite

Columbia Encyclopedia The Columbia Electronic Encyclopedia, Sixth Edition Copyright © 2012, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/. Read

Cite

Wikipedia on Answers.com This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article Equatorial coordinate system. Read

Answer these

Which coordinate in the equatorial coordinate system is like longitude in the geographic coordinate system?

Who relies on the equatorial coordinate system the most?

Why do astronomers prefer the equatorial coordinate system?

What is coordinate plane or coordinate system?

» more

Featured guides

» More

Mentioned in

declination (in astronomy)

right ascension (in astronomy)

hour circle (in astronomy)

celestial pole (in astrophysics)

equator (in geography)